This is how I play it and it seems to fit well.
(X) = Palm Mute
^ = Bend 1/2 note
H = hammer on
P = pull off
~ = Vibrato
/ = slide
Intro:
E|-----------------------------------------------------------|
B|-----------------------------------------------------------|
G|-------5---------------7-5---------------------------------|
D|---5-7---7-(7)-(7)-(7)------7----5-----------------------5-|
A|-7-----------------------------7---7-(7)-(7)-(7)-5H7P5H7---|
E|-----------------------------------------------------------|
E|----------------------------------------------------------|
B|----------------------------------------------------------|
G|---5---------------7^-7^-7^-5-----------------------------|
D|-7---7-(7)-(7)-(7)------------7---5-------------------5-5-|
A|--------------------------------7---7-(7)-(7)-(7)-5-7-----|
E|----------------------------------------------------------|
E|-----------------------------------------------------------|
B|-------------------------------------------------8-5-------|
G|-------5---------------7-5---------------------------5-7-5-|
D|-----7---7-(7)-(7)-(7)------7----5-------------------------|
A|-------------------------------7---7-(7)-(7)---------------|
E|-----------------------------------------------------------|
E|-----------------------------------------------------------|
B|-----------------------------------------------------------|
G|-------5---------------7-5---------------------------------|
D|-----7---7-(7)-(7)-(7)------7----5-----------------------5-|
A|-------------------------------7---7-(7)-(7)-(7)-5H7P5H7---|
E|-----------------------------------------------------------|
Verse:
E|-----------------------------------------------------------|
B|-----------------------------------------------------------|
G|----5------------------------------------------------------|
D|--7---7-(7)-(7)-(7)-(7)-(7)-(7)---5----------------------5-|
A|--------------------------------7---7-(7)-(7)-(7)-(7)-(7)--|
E|-----------------------------------------------------------|
E|-----------------------------------------------------------|
B|-------------------------------------------------8-5~~-----|
G|----5--------------------------------------------------7---|
D|--7---7-(7)-(7)-(7)-(7)-(7)-(7)---5------------------------|
A|--------------------------------7---7-(7)-(7)-(7)----------|
E|-----------------------------------------------------------|
E|-----------------------------------------------------------|
B|-----------------------------------------------------------|
G|----5------------------------------------------------------|
D|--7---7-(7)-(7)-(7)-(7)-(7)-(7)---5----------------------5-|
A|--------------------------------7---7-(7)-(7)-(7)-(7)-(7)--|
E|-----------------------------------------------------------|
E|-----------------------------------------------------------|
B|-----------------------------------------------------------|
G|----5------------------------------------------------------|
D|--7---7-(7)-(7)-(7)-(7)-(7)-(7)---5----------------------5-|
A|--------------------------------7---7-(7)-(7)-(7)-5H7P5H7--|
E|-----------------------------------------------------------|
Chorus:
E|-------------------------------/10-8-5H8P5-------------|
B|-5~~--7~~--5~~---5~~--7~~--5~~-------------8---5-------|
G|-7~~--9~~--7~~---7~~--9~~--7~~---------------7---7-----|
D|-7~~--9~~--7~~---7~~--9~~--7~~-----------------------5-|
A|-5~~--7~~--5~~---5~~--7~~--5~~---------------------7---|
E|-------------------------------------------------------|
Post Chorus:
E|-----------------------------------------------------------|
B|-----------------------------------------------------------|
G|-------5---------------7-5---------------------------------|
D|-----7---7-(7)-(7)-(7)------7----5-----------------------5-|
A|-------------------------------7---7-(7)-(7)-(7)-5H7P5H7---|
E|-----------------------------------------------------------|
E|-----------------------------------------------------------|
B|-----------8-5---------------------------------------------|
G|-------5-------7-5-----------------------------------------|
D|-----7---7--------------5-----------------------5----------|
A|----------------------7---7-(7)-(7)-(7)-5H7P5H7------------|
E|-----------------------------------------------------------|
Verse
Chorus:
E|-------------------------------/10-8-5H8P5-------------|
B|-5~~--7~~--5~~---5~~--7~~--5~~-------------8---5-------|
G|-7~~--9~~--7~~---7~~--9~~--7~~---------------7---7-----|
D|-7~~--9~~--7~~---7~~--9~~--7~~-----------------------5-|
A|-5~~--7~~--5~~---5~~--7~~--5~~---------------------7---|
E|-------------------------------------------------------|
[ Tab from: https://www.guitartabs.cc/tabs/b/black_keys/the_flame_tab_ver_4.html ]
Solo:
E|--------------------------------------------------------|
B|----------------------------------------8-5-------------|
G|---5-7P5------------------------------------7-5----5----|
D|-7-------7-(7)-(7)-7--5------5-------------------7---7--|
A|---------------------------7---7-(7)-(7)----------------|
E|--------------------------------------------------------|
E|-----------------------------------------------5-8-10-8---------|
B|-----5----------------------------------5~-5-8----------10-8----|
G|-5-7---7-5-7-5-5-------5------------5-7----------------------9/7|
D|-------------------5-7---7-/9-9-9-7-----------------------------|
A|-----------------7----------------------------------------------|
E|----------------------------------------------------------------|
E|-------------------------------------------------------------------|
B|------------------------------------8-10-8-------------------------|
G|-----------------------7~-5-7-5-7/9--------9---------5H7-----------|
D|---5-7-7~-5-----5-7~---------------------------5---7----7-5--------|
A|-7----------7-7------------------------------7---7----------7-7-5~-|
E|-------------------------------------------------------------------|
E|---------------------------------------------------------------------|
B|-------8-5------------------------------5----------------------------|
G|---5-------5-7-5-------------5~---5---7^---7^-7-5--------------------|
D|-7---7-------------5------------7---7-------------7---5----------5-7-|
A|-----------------7---7-5H7-7------------------------7---7-5H7P5H7----|
E|---------------------------------------------------------------------|
Verse:
E|-----------------------------------------------------------|
B|-----------------------------------------------------------|
G|----5------------------------------------------------------|
D|--7---7-(7)-(7)-(7)-(7)-(7)-(7)---5----------------------5-|
A|--------------------------------7---7-(7)-(7)-(7)-(7)-(7)--|
E|-----------------------------------------------------------|
E|-----------------------------------------------------------|
B|--------------------------------------------------8--------|
G|----5-----------------------------------------------7^-7---|
D|--7---7-(7)-(7)-(7)-(7)-(7)-(7)---5------------------------|
A|--------------------------------7---7-(7)-(7)-(7)----------|
E|-----------------------------------------------------------|
E|-----------------------------------------------------------|
B|-----------------------------------------------------------|
G|----5------------------------------------------------------|
D|--7---7-(7)-(7)-(7)-(7)-(7)-(7)---5----------------------5-|
A|--------------------------------7---7-(7)-(7)-(7)-(7)-(7)--|
E|-----------------------------------------------------------|
E|-----------------------------------------------------------|
B|---------------------------------------------------8-------|
G|----5------------------------------------------------------|
D|--7---7-(7)-(7)-(7)-(7)-(7)-(7)---5---------------------5--|
A|--------------------------------7---7-(7)-(7)-(7)---5/7----|
E|-----------------------------------------------------------|
Chorus:
E|------------------------------------8------------------|
B|-5~~--7~~--5~~---5~~--7~~--5~~--/10---10-8-------------|
G|-7~~--9~~--7~~---7~~--9~~--7~~-------------9-5-7-5---5-|
D|-7~~--9~~--7~~---7~~--9~~--7~~---------------------5---|
A|-5~~--7~~--5~~---5~~--7~~--5~~-------------------------|
E|-------------------------------------------------------|
Outro:
E|------------------------------------------------------------|
B|----------------------------8-5--------------8-5------------|
G|---5--------------------5-------5H7-5-------------7-5-7-5---|
D|-7---7-/7-5---5-------7---7-------------5-----------------7-|
A|------------7---7-5H7-----------------7---7-----------------|
E|------------------------------------------------------------|
E|----------------------------------------------------------------------|
B|-----------------5------------/5-5---/5-5-----------8-5---------------|
G|---5-------5-7-7---7---------------7------7-5---5-------7-5-------5---|
D|-7---7-5H7-------------5----------------------7---7---------7-5-7---7-|
A|---------------------7---7--------------------------------------------|
E|---------------------------0------------------------------------------|
E|-------------------------------------|
B|---------------5/7---7/10---10-------|
G|---------------7/9---9/11---11-5~----|
D|---5-------5---7/9---9/11---11-7~----|
A|-7--7--5H7-----5/7---7/10---10-7~----|
E|-------------5-----------------5~----|
I hope you enjoy it, leave any comments about what you think should be changed. Thank you.